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    {
      "cell_type": "code",
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        "%matplotlib inline"
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      "source": [
        "\n# Joint feature selection with multi-task Lasso\n\n\nThe multi-task lasso allows to fit multiple regression problems\njointly enforcing the selected features to be the same across\ntasks. This example simulates sequential measurements, each task\nis a time instant, and the relevant features vary in amplitude\nover time while being the same. The multi-task lasso imposes that\nfeatures that are selected at one time point are select for all time\npoint. This makes feature selection by the Lasso more stable.\n\n\n"
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      "source": [
        "print(__doc__)\n\n# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>\n# License: BSD 3 clause\n\nimport matplotlib.pyplot as plt\nimport numpy as np\n\nfrom sklearn.linear_model import MultiTaskLasso, Lasso\n\nrng = np.random.RandomState(42)\n\n# Generate some 2D coefficients with sine waves with random frequency and phase\nn_samples, n_features, n_tasks = 100, 30, 40\nn_relevant_features = 5\ncoef = np.zeros((n_tasks, n_features))\ntimes = np.linspace(0, 2 * np.pi, n_tasks)\nfor k in range(n_relevant_features):\n    coef[:, k] = np.sin((1. + rng.randn(1)) * times + 3 * rng.randn(1))\n\nX = rng.randn(n_samples, n_features)\nY = np.dot(X, coef.T) + rng.randn(n_samples, n_tasks)\n\ncoef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])\ncoef_multi_task_lasso_ = MultiTaskLasso(alpha=1.).fit(X, Y).coef_\n\n# #############################################################################\n# Plot support and time series\nfig = plt.figure(figsize=(8, 5))\nplt.subplot(1, 2, 1)\nplt.spy(coef_lasso_)\nplt.xlabel('Feature')\nplt.ylabel('Time (or Task)')\nplt.text(10, 5, 'Lasso')\nplt.subplot(1, 2, 2)\nplt.spy(coef_multi_task_lasso_)\nplt.xlabel('Feature')\nplt.ylabel('Time (or Task)')\nplt.text(10, 5, 'MultiTaskLasso')\nfig.suptitle('Coefficient non-zero location')\n\nfeature_to_plot = 0\nplt.figure()\nlw = 2\nplt.plot(coef[:, feature_to_plot], color='seagreen', linewidth=lw,\n         label='Ground truth')\nplt.plot(coef_lasso_[:, feature_to_plot], color='cornflowerblue', linewidth=lw,\n         label='Lasso')\nplt.plot(coef_multi_task_lasso_[:, feature_to_plot], color='gold', linewidth=lw,\n         label='MultiTaskLasso')\nplt.legend(loc='upper center')\nplt.axis('tight')\nplt.ylim([-1.1, 1.1])\nplt.show()"
      ]
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